Freefall and the observation of low frequency gravitational waves with LISA

1
Free-fall and the observation of low frequency
gravitational waves with LISA Bill
Weber Università di Trento Caltech March 24,
2006
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LISA
Laser Interferometer Space Antenna
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LISA an orbiting observatory for low frequency
gravitational waves
Sensitivity curve for 1 year integration and
S/N5
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Purity of free-fall critical to LISA science
Example massive black hole (MBH)
mergers Integrated SNR at 1 week intervals for
year before merger
Assuming LISA goal Sa1/2 lt 3 fm/s2/Hz1/2 at 0.1
mHz

• Factor 10 in acceleration noise ?decreased
  observation time (year ?weeks)
• LISA sweeps out only 10 degrees rather than a
  full circle
• Lose information on source location and thus
  source luminosity distance

How guaranteed is LISAs low frequency
sensitivity and projected scientific return?
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• What are the sources of force noise that can
  compromise purity of free-fall for LISA?
• What is the proposed drag-free control system
  that aims to minimize force noise?
• What do we know and what can we learn
  quantitatively about these sources of force
  noise?
• ? LISA Pathfinder in-flight test
• ? torsion pendulum studies on the ground

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Stray forces and drag-free control

• Solar radiation pressure would give 10 nm / s2
  acceleration to 1 kg test mass

mNewton Thrusters Drag Free loop gain MwDF2
m
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Key LISA test mass acceleration noise sources
dx
Gap
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Gravitational Reference Sensor Design

• 1 nm/Hz1/2 sensor noise floor
• low force gradient (k 100 nN/m)
• low force noise (Sf1/2 fN/Hz1/2)

f
xm
k

• 40-50 mm cubic Au / Pt test mass (1-2 kg)
• 6 DOF gap sensing capacitive sensor
• Contact free sensing bias injection
• Resonant inductive bridge readout (100 kHz)
• Audio frequency electrostatic force actuation
• ? avoid DC voltages
• Large gaps (2 4 mm)
• ? limit electrostatic disturbances
• High thermal conductivity metal / ceramic
  construction
• ? limit thermal gradients

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Capacitive sensing readout / actuation scheme
Modeling of position and force noise
VACT1
Cfb
VAC 100 kHz
L
n2L
L
VACT2
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Acceleration noise projections for LISA
Note worst case, assume performance at 0.1
mHz across whole band
How do we verify these predictions for
acceleration noise?
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ESA / NASA LISA Pathfinder Mission Launch
2008 Testing TM free-fall purity to within an
order of magnitude of the LISA goals
LISA ares lt 3 10-15 m/s2/Hz1/2 f gt 0.1
mHz
LTP ares lt 30 10-15 m/s2/Hz1/2 f gt 1 mHz
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LISA Technology Package (LTP) aboard LISA
Pathfinder
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2 Masses, 1 measurement axis (x)
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LTP Measurement of stray force noise fstr
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LTP Measurement of External Force and Sensor Noise

• Closed-loop satellite control nulls the sensor
  1 output to an accuracy limited by the finite
  gain control loop response to external forces

TM1
TM2
Dx1
Fstr
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Drag-free control setpoint modulation stiffness
measurement

• control satellite to TM1 to a modulated
  setpoint x0 sinwt
• control TM2 to follow TM1 (mode 3)
• shake satellite, observe differential motion

• acceleration noise limited differential
  stiffness resolution

• Roughly 2 of LISA stiffness goal of 4 10-7 /s2
• Other schemes allow 10-20 absolute stiffness
  measurement via sensor signal

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Coherent force measurements
Magnetic field effects

• Measurement of disturbance time series allows
  correlation analysis of noise sources,
  measurement of actual coupling parameter allows
  possible correction
• LTP is a true experiment, debuggable

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• LTP instrument noise limit
• resolution with which we can measure LISA force
  noise
• 5 fm/s2/Hz1/2 (within 2 of LISA goal at 1 mHz)
• limited by interferometer and actuation noise

LISA goal
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Torsion pendulum measurements of small forces
originating in gravitational reference sensor
Light-weight test mass suspended as inertial
member of a low frequency torsion pendulum,
surrounded by sensor housing
Measure stray forces as deflections of pendulum
angular rotation to within 100x
LISAgoal, 10x LTP goal
Mirror for Optical Readout

Test Mass inside Sensor Housing
Precision coherent measurement of known
disturbances

Sensing electrodes


1
2

gap


d
Pendulum suspension and axis of rotation
Sensing electrodes
separation

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Results obtained with 2 different sensors
Trento prototype
LTP EM sensor
Design differences Gaps 2 mm ? 4 mm ?
further reduction of short range electrostatic
effects Injection electrodes z-axis ? y and
z axes ? favors x axis Electrode material Au
coated Mo ? Au coated ceramic (shapal) ?
better machining tolerances ? risk of exposed
dielectric Construction techniques HV glue /
screws, pin contacts
LTP Flight Model Sensor Au coated sapphire
electrodes
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Force noise measurements more stringent upper
limits Pendulum angular deflection noise measured
over 3 days
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Force noise upper limits (old sensor)
LTP Goal (most pessimistic torque force
conversion, 10.25 mm)
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Force noise upper limits (new sensor)
LTP Goal
Excess noise observed below 1 mHz ? rises more
steeply than thermal noise Observed with both
sensors ? likely pendulum (not sensor) related ?
Currently under investigation!
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Noise source characterization Stiffness coupling
to spacecraft motion
Move sensor (or spacecraft), measure force (or
torque)

• Coherent torque excited by square wave
  oscillation of sensor rotation angle
• Search for all sources of stiffness, with and
  without sensing bias

Results G GSENS G0 GSENS - 89.2 .5
pN m / rad consistent with expected sensor bias
stiffnes G0 - 12.0 .3 pN m / rad extra
stiffness ... could be explained by 115 mV RMS
patch voltages
SENSOR ON
SENSOR OFF
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Stiffness with 4-mm gap sensor
Sensor ON electrostatic stiffness roughly as
modelled
Sensor OFF stiffness essentially zero ? extra
stiffness not observed
? With 4 mm gap sensor, unmodelled force
gradients are not likely to be an issue for LISA
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Noise source characterization Thermal gradient
measurement

• (Noisy) temperature gradient converts to (noisy)
  force
• radiation pressure
• radiometric effect
• temperature dependent outgassing (???)

In the lab (and on LTP) apply DT ? measure force
(torque)
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Thermal gradient measurement pressure dependence

• radiometric effect as expected
• N(p0) increases with temperature as expected

• measured torque is consistent with
  radiometricradiation pressure effects
• (factor 2 uncertainty in effective DT)

Measured value 1 10-7 mBar Theoretical 1.5
10-7 mBar
Largely independent of DT, geometry

• we actually see too small a torque coefficient
• radiation pressure effect probably
  overestimated (not infinite plates)
• any temperature dependent outgassing effect is
  too small to hurt LISA

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Noise source DC biases
dV1
dV2
VM
Dx
Electrostatic stiffness
Random charge noise mixing with DC bias (Dx)
Noisy average DC bias (SDx) mixing with mean
charge
Noisy DC biases interacting with themselves
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Individual noise source characterization DC Bias
measurement and compensation
Average DC bias difference couples to charge shot
noise

• Apply charge, measure force (extract DV)
• Compensate DV

• DC biases of order 10s of mV would be a
  relevant noise source
• Sub-mV compensation demonstrated with torsion
  pendulum, possible in flight
• Random charging should not be problematic under
  normal conditions

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Noise source in-band voltage noise mixing with
DC bias

• Voltage noise vn
• Actuation amplifier noise (electronics)
• Thermal voltage fluctuations (d)
• Drifting (not Brownian) DC bias SdV1/2

• DC voltage difference dV
• Residual unbalanced patch effects
• Test mass charge

LISA requires vn 20 mV/Hz1/2
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Measurement of dielectric losses new direct
measurement technique
Circuit surface losses
Force (torque) quadratic in voltage
1W
1E
perfect square wave voltage produces only DC
force (torque)
2W
2E
Force
Electrode voltage
No losses
Ohmic delay
d constant
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Measurement of dielectric losses new direct
measurement technique
Application of perfect square wave yields
constant force Any lossy element creates delays
and thus force transients
Direct application (f .4 mHz)
Application through an ohmic delay (t 7 ms, d
2 10-5)
390 kW
19 nF
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Dielectric Loss Angle Measurement Results

• 2w cosine torque frequency dependence ? ohmic
  delay time t 0.3 ms (agrees with calculated
  value)
• 2w sine cosine intercept values ? d 10-6
  (likely not a problem for LISA!!)

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DC Bias measurements stability
4 day measurement of residual DC balance
stability after compensation

• Observe long term drifts in the DC bias
  imbalance of mV over several days

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DC Bias measurements stability
LISA goal

• Limited by pendulum force noise measurement
  resolution above 50 mHz
• excess noise (drifting) below 50 mHz
• current measurement resolution not sufficient to
  guarantee LISA performance!

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Continuous charging with UV light
2 UV fibers ? illuminate TM and/or electrodes for
bipolar photoelectric discharging
TM ONLY
ELECTRODE LAMP 5 TM LAMP 100 Cancelling
charge rates of 35000 /s and -35000 / s
EL ONLY
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Magnetic testing of full Au Pt test mass

• Measuring LISA TM magnetic properties (residual
  moment and susceptibility) with a torsion pendulum

Holder and mirror for optical readout
Applied B field

• Measure moment detection with pendulum deflection
  in homogeneous field

• Measurement of susceptility (c) requires non-zero
  second derivative of B (2f signal, analysis in
  progress)

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Development of Four-mass torsion pendulum

• in LTP / LISA, force matters (not torque!)
• Direct sensitivity to net forces (Fx rather
  than just Nf) not achievable with 1-mass pendulum
  design
• thermal outgassing, DC electrostatic problems
  could arise at central edges of the electrodes
• translational stiffness qualitatively different
  from rotation stiffness with current electrode
  design

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Four-mass pendulum facility construction
Go big() or stay home!
Torque signal
() How big?
Gravitational gradient noise

• First inertial member has arm length R 10 cm
• Gravitational gradient measurements underway

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Four-mass pendulum initial testing with
prototype inertial member

• blank measurement to measure pendulum noise
  in absence of sensor
• ? thermal noise, twist/tilt, temperature
  sensitivity, gravity gradient noise

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Preliminary data 4 mass pendulum
? Pendulum ready to make relevant direct force
measurements for LISA
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LISA low frequency sensitivity goal requires test
masses to be in perfect free-fall to within 3
fm/s2/Hz1/2
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Trento physicists contemplate free fall and free
food while celebrating the PhD of Doctor Ludovico
Carbone
minus Antonella Cavalleri, plus Tim Sumner
Michele Armano Ludovico Carbone Antonella
Cavalleri Giacomo Ciani Rita Dolesi
Mauro Hueller David Tombolato Stefano Vitale Bill
Weber
Trento LTP / LISA Group